J.-L. Auriault

Heat and mass transfer in wet porous media in presence of evaporation—condensation

Abstract The modelling of heat and mass transfer in wet porous media in the presence of evaporation-condensation is revisited by using the homogenization method of asymptotic expansions for periodic structures. In order to produce the ‘upscaled’ equations for the continuum equivalent to the porous medium, we start from the pore level. At this scale the physics is described by convection and Ficks molecular diffusion coupled with heat transfer. The phase change process is incorporated into the analysis. The main advantage of the method is to use a systematic, rigorous and unified treatment to provide a general comprehension of all the interactions involved by the different heat and mass transfers. Four characteristic selected models are carried out. Their domains of validity are determined in function of the relative weight of the different phenomena in presence. Comparison with other models in the literature is presented. It appears that some of them exhibit a similar structure. In particular, the continuous passage between the different macroscopic models is investigated. Finally, the condition for a non-homogenizable situation, i.e., when it is impossible to find a macroscopic equivalent description is also addressed.

Acoustic absorption of porous surfacing with dual porosity

Abstract This paper is devoted to the determination of the acoustic characteristics of a porous medium saturated by air. The analysis of sound propagation in such a medium is performed using an homogenization technique. This theory is suitable since acoustic wavelengths are much greater than the usual pore size. The macroscopic descriptions involve the effects of air viscosity, inertial forces and heat transfer. The first part of the paper deals with single porosity materials. Two cases are investigated : (i) a medium with large pores in which thermal exchanges are negligible ; (ii) a medium with smaller pores for which thermal exchanges must be accounted for. The second part is concerned with dual porosity media, i.e. when the grains themselves are also porous. Neglecting heat transfer first yields a simplified macroscopic description. This simply dual porosity model is then improved by considering thermal effects. These results show that new porous materials could be evolved by introducing a microporosity structure that would give enhanced absorption properties over a wide range of frequencies.

Continuum Modelling of Contaminant Transport in Fractured Porous Media

This work is aimed towards deriving macroscopic models that describe pollutant migration through fractured porous media. A homogenisation method is used, that is, macroscopic models are deduced from the physical description over a representative elementary volume (REV), which consists of an open fracture surrounded by a porous matrix block. No specific geometry is at issue. The fractured porous medium is saturated by an incompressible fluid. At the REVs scale, the transport is assumed to be advective-diffusive in the porous matrix and due to convection and molecular diffusion in the fractures domain. It is also assumed that there is no diffusion in the solid. We demonstrate that the macroscopic behaviour is described by a single-continuum model. Fluid flow is described by Darcys law. Four macroscopic single-continuum models are obtained for the contaminant transport: a diffusive model, an advective-diffusive model and two advective-dispersive models. One of the two advective-dispersive models accounts for the advection process in the porous matrix. The domains of validity of these models are defined by means of the orders of magnitude of the local Péclet numbers in the porous matrix block and in the fractures domain.

Macroscopic modeling of double-porosity reservoirs

Abstract This paper deals with the seepage of a fluid through a fractured porous medium. It summarizes important results obtained using the homogenization method for periodic structures. Thereby, unlike the phenomenological approaches, the macroscopic behaviors are deduced from the physics at the microscopic scales, without any prerequisite. Two cases have been investigated: flow of gas through a rigid medium and flow of incompressible fluid through a deformable matrix. In both situations, it turns out that the ratio between the two separations of scales (macroscopic scale/fissure scale and fissure scale/pore scale) plays an essential role. The macroscopic description depends upon the separations of scales, and the coupling effects between the two porous systems are maximum when the scales are equally separated. Then, the homogenization result is compared to classical phenomenological models for slightly compressible fluid flow through a rigid double-porosity medium. Pseudo-steady-state phenomenological models are shown to give a rough description for transient excitations and finally a correction is proposed giving a more accurate short-time behavior.

Heat Transfer in Nonsaturated Porous Media. Modelling by Homogenisation

This paper is devoted to the modelling of a temperature field in nonsaturated porous media in the absence of phase change. We establish the energy equation at the macroscopic level, from a description at the pore level by using the homogenisation method of multiple-scale asymptotic expansions. Different macroscopic models are obtained depending on the values of the local Péclet number and the local Fourier number. An example of the application of the different model catalogue is presented which concerns the modelling of the hot pressing of a paper web.

Erosion and deposition of solid particles in porous media: Homogenization analysis of a formation damage

The aim of the paper is to model at a large scale, the formation damage in porous media by erosion and deposition of solid particles. We start from the equations governing the pore-scale processes of erosion, deposition, convection and diffusion. The macroscopic equivalent behaviour is investigated by using a homogenization method. Four characteristic models with different dominating phenomena at the pore scale are determined. The main results are twofold: first dispersion-deposition and dispersion-erosion phenomena are shown at the macroscopic scale for peculiar values of the dimensionless numbers; furthermore, and contrarily to phenomenological models, erosion and deposition generally occur in regions of intense and slow flow, respectively.

Acoustics of a porous medium saturated by a bubbly fluid undergoing phase change

The objective of this work is the derivation of the wave equations for describing acoustics in a deformable porous medium saturated by a bubbly fluid, when capillary, thermal and phase change effects are accounted for. This is performed using an homogenisation technique: the macroscopic model is obtained by upscaling the bubble-scale and the pore-scale descriptions. For convenience a bubbly fluid near the bubble point, in the bulk of which a small perturbation can generate small bubbles is considered. Although the derived macroscopic wave equations are similar in their structure to Biots equations that describe wave propagation in saturated porous media, important differences appear as a result of the presence of bubbles. In effect, gas–liquid phase change considerably decreases the apparent rigidity of the bubbly fluid, and consequently decreases the wave velocity in the porous medium. Moreover, this phenomenon is amplified for very small bubbles, for which the apparent rigidity of the bubbly fluid can be negative. The influence of the bubbly liquid apparent rigidity on the wave velocity and attenuation is highlighted on an illustrative example: it is shown that they strongly differ from wave velocities and attenuations in porous media saturated by a liquid or by a gas.

Transient Heat and Solute Transfers in Liquid-Saturated Porous Media

We investigate transient heat and solute transfers in liquid-saturated porous media. The macroscopic equivalent models are obtained by a homogenization process from the pore-scale description. The large value of the Lewis number in liquid mixtures introduces a possible separation of scales between the heat and solute diffusion wavelengths

Does Klinkenberg's law survive upscaling?

L^{\mathrm{heat}}